what is a pi ? how the area of a circle is calculated?

Question

the diameter of a wheel car is 77cm. how many revolutions will it make to cover a distance of 72.6m?

Answer 1

All circles have the same shape with different sizes. Figures that have the same shape are “similar” with their corresponding parts “proportional”. For all circles that means their Circumference to Diameter ratios are equal:

C_1 / D_1 = C_2 / D_2 = C_3 / D_3 = C_4 / D_4 = ... = C_n / D_n := π or pi.

As indicated, this common ratio is defined (:=) as the number π or pi. Note that even though pi is defined as a ratio of numbers it is NOT rational because it is not a ratio of integers; either C_i or D_i MUST be irrational.

A circle can be approximated with a regular polygon with n sides of length s and interior radius r (shortest distance between center and one side). The area of such a regular polygon is (just add up all the triangles):

Area_regPoly = (1/2)nsr.

The Perimeter of the polygon is P = ns.

As n increases to very large numbers, the Regular Polygon looks more and more like a Circle. The Perimeter becomes the Circumference and the Area becomes:

Area_Cirle = (1/2)*C*r = (1/2)*(C/D)*r*D = (1/2)*(pi)*r*(2r)

Area_Cirle = (pi)*r^2 = πr^2

=====

A car wheel with Diameter, D = 77 cm = 0.77 m, has a Circumference, C = π D = π * 0.77 m.

To cover a distance of 72.6 m, the wheel will have to rotate 72.6 m / (π * 0.77 m) ≈ 30.01207498304312 ≈ 30.0 times.

Answer 2

 

 Pi - is the ratio of circumference of a circle to its radius, or ratio of area to the square of its radius.

 

 

        π = pi = C / d = A/( r^2).

 

       Circles with all radius the ratio of their circumference to radius , or the ratio of the  area to the        

 

      square  of the radius is fixed. Therefore:

 

 

         C _{circumference =} 2πr

 

          A _{area =} π(r^2).

 

    C =  77 π = 241.9  Cm / Distance traveled in

                               one revolution.

   

     (7260cm)/ (241.9cm/ revol )= 30 revolution. 

 

           

      

Answer 3

If the diameter of the wheel is 77 cm, then its circumference is 77cm*pi = 241.903cm ot 242 cm.

 

Number of revolutions = 72.6 meters/242 cm

 

Convert numerator to cm (7260)

 

Number of revolutions = 7260cm/242 cm = 30.012 or 30 revolutions

Answer 4

You need circumference or a perimeter of a circle first. You don't need area because the wheel revolves on its edge.

C=pi×d, so 3.14×77=241.78cm 

 

1meter is 100 cm so, 241.78/100=2.4178m and that isa distance for one revolution in meters.

 

72.6÷2.4178=30.02 or around 30 total revolutions on the set distance.

 

fyi: area of a circle A=pi×r²

Answer 5

you first need to find the circumference of the wheel

C=pi*d where pi=3.14159265...and d=77 cm

C=3.14159265*77

C=241.90263 cm

now convert 72.6 m to cm where 1 m=100 cm

72.6 m=7260 cm

now divide 7260 by 241.90263; 7260/241.90263=30.012076 revolutions

by the way pi is the ratio of the circumference of a circle to its diameter which is the same for all circles

pi is an irrational number; a non-ending, non-repeating decimal

we use approximations for pi such as 3.14, 3.14159, 3.1416, and 22/7

 

Answer 6

Hi Ganga;

diameter=77 cm

distance=72.6 m

Our first priority concerns the fact that both these numbers are in different units: cm and m.  Let's convert one.  I randomly choose the first.  One meter is 100 cm.

diameter=0.77 m

distance=72.6 m

The circumference of the circle is distance multiplied by pi, 3.14.

circumference=(0.77 m)(3.14)

distance=72.6 m=(circumference)(x)

x=quantity of revolutions

72.6 m=(0.77 m)(3.14)(x)

72.6 m=(2.42 )(x)

Let's divide both sides by 2.42...

30.0=x